"Single Arrival Behavior in Queueing Models with Removable Servers: A Theoretical Approach" explores the dynamics of queueing systems where servers can be removed or deactivated depending on the system state, specifically in the context of a single arrival process. This study provides a theoretical framework for analyzing such systems, focusing on how server removal influences system performance metrics such as waiting times, queue lengths, and service efficiency. By modeling the system under various assumptions about the arrival process, server availability, and removal conditions, the research investigates how different configurations affect the overall behavior of the queue. The study uses analytical methods and mathematical models to derive key performance indicators and explores the impact of server removal policies on system stability and resource utilization. This approach aims to offer insights into the design and optimization of queueing systems in practical applications, such as telecommunications, healthcare, and manufacturing, where servers may be intermittently available or deactivated based on demand or operational constraints.

Queueing models, removable servers, single arrival

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